Paleoclimate data assimilation with CLIMBER-X: An ensemble Kalman filter for the last deglaciation

Using the climate model CLIMBER-X, we present an efficient method for assimilating the temporal evolution of surface temperatures for the last deglaciation covering the period 22000 to 6500 years before the present. The data assimilation methodology combines the data and the underlying dynamical principles governing the climate system to provide a state estimate of the system, which is better than that which could be obtained using just the data or the model alone. In applying an ensemble Kalman filter approach, we make use of the advances in the parallel data assimilation framework (PDAF), which provides parallel data assimilation functionality with a relatively small increase in computation time. We find that the data assimilation solution depends strongly on the background evolution of the decaying ice sheets rather than the assimilated temperatures. Two different ice sheet reconstructions result in a different deglacial meltwater history, affecting the large-scale ocean circulation and, consequently, the surface temperature. We find that the influence of data assimilation is more pronounced on regional scales than on the global mean. In particular, data assimilation has a stronger effect during millennial warming and cooling phases, such as the Bølling-Allerød and Younger Dryas, especially at high latitudes with heterogeneous temperature patterns. Our approach is a step toward a comprehensive paleo-reanalysis on multi-millennial time scales, including incorporating available paleoclimate data and accounting for their uncertainties in representing regional climates.

Dear Prof. Dr. Yougui Song, Please find enclosed the revised version of our previous submission entitled "Paleoclimate Data Assimilation with CLIMBER-X: An ensemble Kalman filter for the Last Deglaciation" with manuscript number PONE-D-23-19461.We thank you and the reviewer for the valuable comments that helped improve the quality of our manuscript.In this revision, we have carefully addressed the reviewer's comments.A summary of the main modifications and a detailed point-by-point response to the comments from the Reviewer (following the reviewers' order in the decision letter) are given below.Regarding the financial disclosure, our institute, Alfred Wegener Institute, will pay the publication costs.

Ahmadreza Masoum on behalf of all co-authors
Note: To enhance the legibility of this response letter, all the editor's and reviewers' comments are typeset in boxes.

Authors' Response to the Editor
General Comments.I hope this message finds you well.I wanted to extend my sincerest apologies for the delay in the peer review process for your manuscript.
Despite our efforts, we have encountered challenges in securing potential reviewers including those you had suggested, and obtaining comments from reviewers who initially agreed to evaluate your work.By now, we only obtained one feedback, comments.Considering timeliness, we have decided to forward the comments to you.Although this is not the ideal scenario, we believe that the provided feedback can still be valuable to you for making necessary revisions to your manuscript.

Response:
Thank you for your message and sincere apologies for the challenges faced in the peer review process for my manuscript.We understand the difficulties in finding reviewers and appreciate your handling of the review process and your decision to share the obtained feedback despite the limitations.According to the reviewer's comments, we have checked our manuscript and addressed them by adding content to the Experimental Design and Discussion sections of the manuscript.
Moreover, the online DA approach allows us to study the performance of CLIMBER-X, including AMOC, salinity, freshwater, and many other climate parameters.Therefore, we decided to apply a more complex method, online DA, because we are able to do that, and it has the potential to get better results than offline DA.To clarify this point, We added more explanations to the manuscript, lines 164-177.
In reply to the second point, we agree that the time gap between successive observations, 100 years, may exceed the model's predictability.Thus, over 100 years we do not expect that the initial state (previous analysis) has an influence.We have added more explanations to the Discussion section, lines 375-380, and clearly mentioned that the surface temperature is mainly driven by external forcings in our experiments.However, our DA method can use high temporal resolution or artificial observations for different applications.For example, one could apply a 10-year temporal resolution just by interpolating the observation values.Then, the effect of temperature could probably persist.

Comment 2
In the manuscript, the localization radius is set to 5000 km.It seems too small.
In the previous studies, they used large localization radius (such as 25000km and even infinite) to assimilate the global surface temperature.Therefore, I suggest the authors should evaluate the results according to observations and choose the best radius (shown in King et al., 2021, JC).

King et al., A Data Assimilation Approach to Last Millennium Temperature Field
Reconstruction Using a Limited High-Sensitivity Proxy Network

Response:
The localization radius is always case-dependent, and there are different ways to determine an optimal radius.Depending on different factors, such as the prior states, DA approach, observation, and the targets of the articles, the previous studies have defined their own criteria and selected different localization radii.For example, the offline DA reconstructions such as Erb et al. (2022), King et al. (2021), Osman et al. (2021), and Tierney et al. (2021) who use outputs of different coupled general circulation models for generating ensemble priors, select a relatively large radius from 12000 km to 25000 km.However, Okazaki et al. (2021) employ an EMIC for their online DA, using a 2000, 5000, and 8000 km radius.
Our main criterion is the effect of DA on the surface temperature field.During our trials, we found when we increased the radius, the North Atlantic area would be dominated by the observations located in the northwest of North America, and the effect of Greenland's observation would be lost after DA.Therefore, we decided to select a localization radius of 5000 km.Clearly, one could choose another localization radius with different observation networks.We have added further explanations in the Experimental Design, lines 183-190, and Discussion sections, lines 337-341, to address this comment and improve the readability of the paper.